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By Christopher Thomas, Barnett Rich
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Extra resources for Schaum's Outline of Geometry (5th Edition) (Schaum's Outlines Series)
Example text
Hence, mj 1 ϭ mj 2. 8 Applying postulates to statements Complete each sentence and state the postulate that applies. (a) If Harry and Alice are the same age today, then in 10 years _____ ? (b) Since 32°F and 0°C both name the temperature at which water freezes, we know that _____ ? (c) If Henry and John are the same weight now and each loses 20 lb, then _____ ? ? (d) If two stocks of equal value both triple in value, then _____ ? (e) If two ribbons of equal size are cut into five equal parts, then _____ ?
To Prove: /1 Х /4, /2 Х /3 Plan: Prove nI Х nII PROOF: Statements Reasons 1. AB > CD, BC > AD 1. Given 2. AC > AC 2. Reflexive property 3. nI Х nII 3. SSS 4. /1 Х /4, /2 Х /3 s are Х. 4. 2A Principles of Isosceles and Equilateral Triangles PRINCIPLE 1: If two sides of a triangle are congruent, the angles opposite these sides are congruent. ) Thus in nABC in Fig. 3-12, if AB > BC, then /A Х /C. A proof of Principle 1 is given in Chapter 16. Fig. 3-12 PRINCIPLE 2: Fig. 3-13 If two angles of a triangle are congruent, the sides opposite these angles are congruent.
Post . Subst. (b) aϭc bϭd aϩbϭcϩd CD ϭ AB Given Given Add. Post. Subst. (c) m/BAC ϭ m/ DAE m/ 1 ϭ m/ 1 m/ BAC Ϫ m/ 1 ϭ m/ DAE Ϫ m/ 1 m/ 2 ϭ m/5 Given Given Subt. Post. Subst. (d) m/ BAC ϭ m/ BCA m/ 1 ϭ m/3 m/ BAC Ϫ m/ 1 ϭ m/ BCA Ϫ m/3 m/ 2 ϭ m/ 4 Given Given Subt. Post. Subst. Applying postulates 7 and 8 State the conclusions that follow when the multiplication and division axioms are applied to the data in (a) Fig. 2-18 and (b) Fig. 2-19. Fig. 2-18 Fig. 2-19 Solutions (a) If a ϭ b, then 2a ϭ 2b since doubles of equals are equal.